Were the five in the theater mostly in the same place, or scattered around? And... [ consults mental map. ] I suppose that makes sense, since the mirror room is right next to the theater.

Which direction do you think ... everything traveled in?

[ since there's no way to get to the observatory without going through the theater from the promenade, but there are multiple ways into the theater, or failing that they could have just doubled back... there wasn't any mess in the ballroom, was there? ]